17.8 Circuit

The Circuit unit implements various routines for calculating current supplied by an external circuit. The main purpose is to provide a boundary condition for current-driven systems such as a Z-pinch. There are two parameters that may be used by other units for such a boundary condition: circ_IloadOld and circ_IloadNew. These represent the current (in Amperes) at the current time step $n$ before Circuit is called and the current at time step $n+1$ after Circuit has been called, respectively.

Some of the implementations will output useful information to a file named circuit.dat. The subsections that follow describe the different implementations that are currently included in FLASH. To activate a particular implemenation, include the appropriate path in the Config file of your simulation directory.

17.8.1 Constant

In the Constant implementation is the simplest of the models and applies a constant current to the load. A constant current is useful when considering ideal cases or if actual data from a run is not available. A run time parameter that is defined by the circcurrConstant variable sets the current. By setting this value in the par file this constant current will be applied to the load for the duration of the simulation.
This implementation lies in the physics/sourceTerms/Circuit/ CircuitMain/Constant directory.

17.8.2 FileInput

The FileInput implementation reads in current data from a file, interpolates the data, and then applies the current to the load. The file input mode is useful when the exact properties of the current delivered to the load are known, but not much else about the system.
This unit works by taking in a run time parameter circcurrFile in the flash.par which is the name of the file with the current and time data. The data should be given in MegaAmperes and nanoseconds. The unit first checks to make sure that the file exists. After running the check, a linear interpolation is used to obtain the current values for the simulation time which is then the current that is applied to the load.
This implementation lies in the physics/sourceTerms/Circuit/ CircuitMain/FileInput directory.

17.8.3 McBride

The McBride circuit model follows the work done by McBride et al Phys. Rev. ST Accel. Beams 13, 120401, 20102. This model is a purely reactive model that allows an input current which will be applied to a dynamic load.

Figure 17.21: Schematic showing the circuit that is being solved in the McBride implemenation.

This unit works by taking in a run time parameter circvoltFile in the flash.par which is the name of the file with the voltage and time data. The data should be given in Amps and seconds. As in FileInput, this unit checks if the file exists and then linearly interpolates the data. The obtained voltage is then applied as Voc to the following circuit LC circuit as seen in Figure 17.21. To calculate the current that is applied to the load the following equations are solved:

$$\begin{pmatrix} \frac{dV_c}{dt} [6pt] \frac{dI_{stack}}{dt} ... ... \frac{-V_c-Z_o I_{stack}+V_{oc}}{L} [6pt] \frac{V_c-V_t}{L_o} \end{pmatrix}.$$ (17.280)

Vt can be rewritten as

$$V_t = - \frac{d \Phi}{dt} = -\frac{\Phi^{new}-\Phi^{old}}{dt}$$ (17.281)

where $\Phi$ is the magnetic flux in the domain. In the case of a one dimensional cylindrical domain there is a run time parameter circcylLength which is the length of the cylinder used for the flux calculation. The axial load current that is determined from the circuit model is used with Ampere’s Law to define the azimuthal magnetic field on the upper-r domain boundary. This field is used as a boundary condition for the implicit magnetic resistivity (diffusion) solver.
This implementation lies in the physics/sourceTerms/Circuit/CircuitMain/McBride directory.

17.8.4 CESZAR

The Ceszar circuit model replicates a simplified model of the Ceszar Linear Transformer Driver. Unlike the McBride model, this model is both reactive and resistive driven by a discharging capacitor specified by its initial voltage. The target is a dynamic load.

Figure 17.22: Schematic showing the circuit that is being solved in the Ceszar implemenation.

This unit works by taking in a run time parameter circCESZAR V0 in the flash which defines the voltage across the capacitor in Volts. To calculate the current applied to the load the following equations are solved:

$$\begin{pmatrix} \frac{dI_s}{dt} [6pt] \frac{dI_l}{dt} [6pt] ... ...] \frac{I_s R - I_l (Z_l + R) - V_t}{L_l} [6pt] \frac{-I_s}{C} \end{pmatrix}.$$ (17.282)

Vt can be rewritten as

$$V_t = - \frac{d \Phi}{dt} = -\frac{\Phi^{new}-\Phi^{old}}{dt}$$ (17.283)

where $\Phi$ is the magnetic flux in the domain. In the case of a one dimensional cylindrical domain there is a run time parameter circcylLength which is the length of the cylinder. The axial load current that is determined from the circuit model is used with Ampere’s Law to define the azimuthal magnetic field on the upper-r domain boundary. This field is used as a boundary condition for the implicit magnetic resistivity (diffusion) solver.
This implementation lies in the physics/sourceTerms/Circuit/CircuitMain/CESZAR directory.